Let S be an ideal of subsets of a metric space (X, d). A net of subsets (Aλ) of X is called S-convergent to a subset A of X if for each S ∈ S and each ε > 0, we have eventually A ∩ S ⊆ A <sub>λ</sub><sup>ε</sup> and Aλ ∩ S ⊆. A <sup>ε</sup>. We identify necessary and sufficient conditions for this convergence to be admissible and topological on the power set of X. We show that S-convergence is compatible with a pseudometrizable topology if and only if S has a countable base and each member of S has an ε-enlargement that is again in S. Further, in the case that the ideal is a bornology, we show that S-convergence when pseudometrizable is Attouch-Wets convergence with respect to an equivalent metric.
Beer, G., & Levi, S. (2008). Pseudometrizable bornological convergence is Attouch-Wets convergence. JOURNAL OF CONVEX ANALYSIS, 15(2), 439-453.
Citazione: | Beer, G., & Levi, S. (2008). Pseudometrizable bornological convergence is Attouch-Wets convergence. JOURNAL OF CONVEX ANALYSIS, 15(2), 439-453. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Titolo: | Pseudometrizable bornological convergence is Attouch-Wets convergence |
Autori: | Beer, G; Levi, S |
Autori: | |
Data di pubblicazione: | 2008 |
Lingua: | English |
Rivista: | JOURNAL OF CONVEX ANALYSIS |
Appare nelle tipologie: | 01 - Articolo su rivista |